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    "# Reference: https://jupyterbook.org/interactive/hiding.html\n",
    "# Use {hide, remove}-{input, output, cell} tags to hiding content\n",
    "\n",
    "import sys\n",
    "import os\n",
    "if not any(path.endswith('textbook') for path in sys.path):\n",
    "    sys.path.append(os.path.abspath('../../..'))\n",
    "from textbook_utils import *"
   ]
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   "metadata": {},
   "source": [
    "# Basics of Prediction Intervals\n",
    "\n"
   ]
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Confidence intervals convey the accuracy of an estimator, but sometimes we want the accuracy of a prediction for a future observation. For example, someone might say: half the time my bus arrives at most three-quarters of a minute late, but how late might it get? As another example, the California Department of Fish and Wildlife sets the minimum catch size for Dungeness crabs at 146 mm, and a recreational fishing company might wonder how much bigger than 146 mm their customer's catch might be when they bring them fishing. And for another example, a vet estimates the weight of a donkey to be 169 kg based on its length and girth and uses this estimate to administer medication. For the donkey's safety, the vet is keen to know how different the donkey's real weight might be from this estimate.  \n",
    "\n",
    "What these examples have in common is an interest in the prediction of a future observation and the desire to quantify how far that future observation might be from this prediction. Just like with confidence intervals, we compute the statistic (the estimator) and use it in making the prediction,\n",
    "but now we're interested in typical deviations of future observations from the prediction. \n",
    "In the following sections, we work through examples of prediction intervals based on quantiles, standard deviations, and those conditional on covariates. Along the way, we provide additional information about the typical variation of observations about a prediction.  "
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "## Example: Predicting Bus Lateness \n",
    "\n",
    "{numref}`Chapter %s <ch:modeling>` models the lateness of a Seattle bus in arriving at a particular stop. We observed that the distribution was highly skewed and chose to estimate the typical lateness by the median, which was 0.74 minutes. We reproduce the sample histogram from that chapter here."
   ]
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   "source": [
    "times = pd.read_csv(\"data/seattle_bus_times_NC.csv\")\n",
    "fig = px.histogram(times, x=\"minutes_late\", width=350, height=250)\n",
    "fig.update_xaxes(range=[-12, 60], title_text=\"Minutes late\")\n",
    "fig"
   ]
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  {
   "cell_type": "markdown",
   "metadata": {},
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    "The prediction problem addresses how late a bus might be. While the median is informative, it doesn't provide information about the skewness of the distribution. That is, we don't know how late the bus might be. The 75th percentile, or even the 95th percentile, would add useful information to consider. We compute those percentiles here:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "median:          0.74 mins late\n",
      "75th percentile: 3.78 mins late\n",
      "95th percentile: 13.02 mins late\n"
     ]
    }
   ],
   "source": [
    "print(f\"median:          {times['minutes_late'].median():.2f} mins late\")\n",
    "print(f\"75th percentile: {np.percentile(times['minutes_late'], 75.0, method='lower'):.2f} mins late\")\n",
    "print(f\"95th percentile: {np.percentile(times['minutes_late'], 95.0, method='lower'):.2f} mins late\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From these statistics, we learn that while more than half the time the bus is not even a minute late, one-quarter of the time it's almost four minutes late, and with some regularity it can happen that the bus is nearly 15 minutes late. These three values together help us make plans."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Predicting Crab Size\n",
    "\n",
    "Fishing for Dungeness crabs is highly regulated, including limiting the shell size to 146 mm in width for crabs caught for recreation. To better understand the distribution of shell size of Dungeness crabs, the California Department of Fish and Wildlife worked with commercial crab fishers from Northern California and Southern Oregon to capture, measure, and release crabs. Here is a histogram of crab shell sizes for the approximately 450 crabs caught:    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "tags": [
     "hide-input"
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   "outputs": [],
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    "def subset_and_rename(df):\n",
    "    df = df[[\"presz\", \"inc\"]]\n",
    "    df.columns = [\"shell\", \"inc\"]\n",
    "    return df\n",
    "\n",
    "crabs = (\n",
    "    pd.read_csv(\"data/crabs.data\", delimiter=r\"\\s+\")\n",
    "    .pipe(subset_and_rename)\n",
    "    .query(\"shell > 100 and inc > 8\")\n",
    ")"
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  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "tags": [
     "remove-input"
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     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "px.histogram(crabs, x='shell', nbins=50,\n",
    "             labels=dict(shell='Dungeness crab shell width (mm)'),\n",
    "             width=350, height=250)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The distribution is somewhat skewed left, but the average and standard deviations are reasonable summary statistics of the distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    452.00\n",
       "mean     131.53\n",
       "std       11.07\n",
       "Name: shell, dtype: float64"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "crabs['shell'].describe()[:3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The average, 132 mm, is a good prediction for the typical size of a crab. However, it lacks information about how far an individual crab may vary from the average. The standard deviation can fill in this gap."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In addition to the variability of individual observations about the center of the distribution, we also take into account the variability in our estimate of the mean shell size. We can use the bootstrap to estimate this variability, or we can use probability theory (we do this in the next section) to show that the standard deviation of the estimator is $SD(pop)/\\sqrt{n}$.\n",
    "We also show, in the next section, that these two sources of variation combine as follows:\n",
    "\n",
    "$$\n",
    "\\sqrt{SD(pop)^2 + \\frac {SD(pop)^2}{n}} ~=~ SD(pop) \\sqrt{1 + \\frac {1}{n}}\n",
    "$$\n",
    "\n",
    "We substitute $SD(sample)$ for $SD(pop)$ and apply this formula to our crabs: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11.073329460297957"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.std(crabs['shell']) * np.sqrt(1 + 1/len(crabs))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that including the SE of the sample average essentially doesn't change the prediction error because the sample is so large. We conclude that crabs routinely differ from the typical size of 132 mm by 11 to 22 mm. This information is helpful in developing policies around crab fishing to maintain the health of the crab population and to set expectations for the recreational fisher. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Predicting the Incremental Growth of a Crab"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After Dungeness crabs mature, they continue to grow by casting off their shell and building a new, larger one to grow into each year; this process is called _molting_. The California Department of Fish and Wildlife, wanted a better understanding of crab growth so that they could set better limits on fishing that would protect the crab population. The crabs caught in the study mentioned in the previous example were about to molt, and in addition to their size, the change in shell size from before to after molting was also recorded:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
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       "       shell  inc\n",
       "shell    1.0 -0.6\n",
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   "source": [
    "crabs.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These two measurements are negatively correlated, meaning that the larger the crab, the less they grow when they molt. We plot the growth increment against the shell size to determine whether the relationship between these variables is roughly linear:  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
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          126,
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          135,
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          138,
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font-size: 14px; fill: rgb(36, 36, 36); opacity: 1; font-weight: normal; white-space: pre;\">Dungeness crab shell width (mm)</text></g><g class=\"g-ytitle\" transform=\"translate(4.9248046875,0)\"><text class=\"ytitle\" transform=\"rotate(-90,10.075000000000003,100.5)\" x=\"10.075000000000003\" y=\"100.5\" text-anchor=\"middle\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 14px; fill: rgb(36, 36, 36); opacity: 1; font-weight: normal; white-space: pre;\">Growth (mm)</text></g></g></svg>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "px.scatter(crabs, y='inc', x= 'shell', width=350, height=250,\n",
    "          labels=dict(shell='Dungeness crab shell width (mm)',\n",
    "                     inc='Growth (mm)'),)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The relationship appears linear, and we can fit a simple linear model to explain the growth  increment by the pre-molt size of the shell. For this example, we use the `statsmodels` library, which provides prediction intervals with `get_prediction`. We first set up the design matrix and response variable, and then we use least squares to fit the model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Increment estimate = 29.80 +  -0.12 x Shell Width\n"
     ]
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "\n",
    "X = sm.add_constant(crabs[['shell']])\n",
    "y = crabs['inc']\n",
    "\n",
    "inc_model = sm.OLS(y, X).fit()\n",
    "\n",
    "print(f\"Increment estimate = {inc_model.params[0]:0.2f} + \", \n",
    "      f\"{inc_model.params[1]:0.2f} x Shell Width\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When modeling, we create prediction intervals for given values of the explanatory variable.  For example, if a newly caught crab is 120 mm across, then we use our fitted model to predict its shell's growth.\n",
    "\n",
    "As in the previous example, the variability of our prediction for an individual observation includes the variability in our estimate of the crab's growth and the crab-to-crab variation in shell size. Again, we can use the bootstrap to estimate this variation, or we can use probability theory to show that these two sources of variation combine as follows:\n",
    "\n",
    "$$\n",
    "SD(\\mathbf{e}) \\sqrt{1 + \\mathbf{x}_0 (\\textbf{X}^\\top \\textbf{X})^{-1}\\mathbf{x}_0^\\top} \n",
    "$$\n",
    "\n",
    "Here $\\textbf{X}$ is the design matrix that consists of the original data, $\\mathbf{e}$ is the $n \\times 1$ column vector of residuals from the regression, and $\\mathbf{x}_0$ is the $1 \\times (p + 1)$ row vector of features for the new observation (in this example, these are $\\left[1, 120\\right]$):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>const</th>\n",
       "      <th>shell</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>120</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   const  shell\n",
       "0      1    120"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_data = dict(const=1, shell=120)\n",
    "new_X = pd.DataFrame(new_data, index=[0])\n",
    "new_X"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use the `get_prediction` method in `statsmodels` to find a 95% prediction interval for a crab with a 120 mm shell: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
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       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>mean_se</th>\n",
       "      <th>mean_ci_lower</th>\n",
       "      <th>mean_ci_upper</th>\n",
       "      <th>obs_ci_lower</th>\n",
       "      <th>obs_ci_upper</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>15.86</td>\n",
       "      <td>0.12</td>\n",
       "      <td>15.63</td>\n",
       "      <td>16.08</td>\n",
       "      <td>12.48</td>\n",
       "      <td>19.24</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    mean  mean_se  mean_ci_lower  mean_ci_upper  obs_ci_lower  obs_ci_upper\n",
       "0  15.86     0.12          15.63          16.08         12.48         19.24"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pred = inc_model.get_prediction(new_X)\n",
    "pred.summary_frame(alpha=0.05)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we have both a confidence interval for the average growth increment for a crab with a 120 mm shell, \\[15.6, 16.1\\], and a prediction interval for the growth increment, \\[12.5, 19.2\\]. The prediction interval is quite a bit wider because it takes into account the variation in individual crabs. This variation is seen in the spread of the points about the regression line, which we approximate by the SD of the residuals. The correlation between shell size and growth increment means that the variation in a growth increment prediction for a particular shell size is smaller than the overall SD of the growth increment: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Residual SD:    1.71\n",
      "Crab growth SD: 2.14\n"
     ]
    }
   ],
   "source": [
    "print(f\"Residual SD:    {np.std(inc_model.resid):0.2f}\")\n",
    "print(f\"Crab growth SD: {np.std(crabs['inc']):0.2f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The intervals provided by `get_prediction` rely on the normal approximation to\n",
    "the distribution of growth increment. That's why the 95% prediction interval\n",
    "endpoints are roughly twice the residual SD away from the prediction. In the\n",
    "next section, we dive deeper into these calculations of standard\n",
    "deviations, estimators, and predictions. We also discuss some of the\n",
    "assumptions that we make in calculating them.  "
   ]
  }
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